Coupled Mode and Parametric Electronics by W H Louisell

By W H Louisell

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The Ei Ji term is related to the kinetic power flow on the beam and is the rate of doing work by the electric force on the currents. The last two terms represent the average magnetic and electric energy stored per unit vol ume of the electromagnetic field. The small signal Poynting theorem is used to derive the kinetic power theorems in later chapters when the beam is coupled to a circuit. The kinetic power theorems play an essential role in determining the coupling coefficients in the coupled mode formulations of various microwave de vices to be treated.

995-1044 (September 1955). W. W. Mumford, "Directional Couplers," Proc. IRE, 35, 160-165 (February 13. 1947). S. E. 14. IRE, H. J. Miller and W. W. Mumford, 40, 1071-1078 Riblet, 1307-1313 "A (September "Multielement 1952). Directional Couplers," Proc. Mathematical Theory of Directional Couplers," Proc. IRE, 35, (November 1947). 15. R. Kompfner, "Experiments on Coupled Helices," AERE Rept. No. G/M98 (September 1951). 16. R. Kompfner, "Coupled Helices," presented at IRE Annual Conference on Elec tron Tube Research, Stanford, Calif.

7 General Approach to Coupling of Two Lossless Modes of Propagation. Consider two waves with time coupled mode form. which are weakly coupled. 57) da2 c2lai (b) ci2 and c2i are the mutual coupling coefficients per unit length. The assumed uniform over the length of the coupler, so that c12 coupling and c2i are independent of length. The modes are assumed lossless. In the absence of coupling, j8x and /32 are positive, the phase velocities of both waves are in the positive z-direction; /3i and /32 are negative, if if is The if the phase velocities are in the negative z-direction; and /3i and /32 are of opposite sign the phase velocities are in opposite directions.

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